cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A014976 Successive locations of zeros in decimal expansion of Pi (where locations 1, 2, 3, ... correspond to digits 3, 1, 4, ...).

Original entry on oeis.org

33, 51, 55, 66, 72, 78, 86, 98, 107, 117, 122, 129, 133, 147, 160, 165, 168, 177, 196, 208, 246, 249, 265, 271, 288, 292, 308, 309, 312, 328, 331, 341, 358, 361, 362, 367, 370, 376, 399, 404, 409, 422, 444, 452, 494, 514, 521, 524, 544, 546, 553, 558, 562, 597, 602, 603, 604, 619, 639, 658
Offset: 1

Views

Author

Bagirath R. Krishnamachari (bagi(AT)callisto.miel.mot.com)

Keywords

Links

Crossrefs

Cf. A000796 (decimal expansion (or digits) of Pi).
Cf. A053745 - A053753 (similar for digits 1 through 9).
Cf. A037008 for a variant with all values decreased by 1.
See A088563 for primes in this sequence.

Programs

  • Maple
    f := proc(n) if pi[n]=0 then n fi; end;[seq(f(i),i=1..2000)]; # where pi is an array with the digits of Pi. - Simon Plouffe [Corrected by Neven Juric, Jul 08 2008]
  • Mathematica
    Flatten[ Position[ RealDigits[Pi, 10, 660] [[1]], 0]] (* Robert G. Wilson v, Mar 19 2004 *)
  • PARI
    A014976_upto(N=999)={localprec(N+20); select(d->!d, digits(Pi\10^-N), 1)} \\ Returns a "Vecsmall": use Vec(...) if needed, or alternatively: {...; [i|i<-[1..#N=digits(Pi\10^-N)], !N[i]]}. - M. F. Hasler, Jul 28 2024

Formula

a(n) = A037008(n) + 1. - Georg Fischer, May 31 2021

Extensions

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

A088565 Primes p such that the p-th digit in the decimal expansion of Pi is 1.

Original entry on oeis.org

2, 41, 139, 149, 199, 239, 251, 397, 433, 439, 443, 491, 569, 599, 641, 647, 661, 787, 853, 883, 1031, 1087, 1097, 1153, 1187, 1319, 1423, 1613, 1619, 1637, 1657, 1667, 1697, 1759, 1789, 2081, 2129, 2143, 2221, 2239, 2459, 2633, 2689, 2741, 2753, 2777
Offset: 1

Views

Author

Cino Hilliard, Nov 19 2003

Keywords

Examples

			The 1st digit 1 in Pi is in the 2nd place of the digits 3,1,4,1,5,9,..., and 2 is prime, whence a(1) = 2.  [Corrected and edited by _M. F. Hasler_, Jul 29 2024]

Links

Crossrefs

Primes in A014976.
Cf. A088563, A088566 (the same for digits 0 and 2), A000796 (decimal digits of Pi).

Programs

  • Mathematica
    Select[Flatten[Position[RealDigits[Pi,10,2800][[1]],1]],PrimeQ] (* Harvey P. Dale, May 05 2019 *)
  • PARI
    pizeros(n,d) = { default(realprecision,5000); p = Pi; v = Vec(Str(p)); for(x=1,n, if(v[x] == Str(d) && isprime(x-1),print1(x-1",")) ) }
  • PARI
    A088565_upto(N=3456, d=1)={localprec(N+20); [p|p<-primes([1, #N=digits(Pi\10^-N)]), N[p]==d]} \\ M. F. Hasler, Jul 29 2024

A088566 Primes p such that the p-th digit in the decimal expansion of Pi is 2.

Original entry on oeis.org

7, 17, 29, 103, 113, 137, 281, 293, 457, 463, 547, 601, 631, 823, 1051, 1091, 1109, 1201, 1231, 1283, 1301, 1327, 1399, 1427, 1447, 1487, 1523, 1621, 1663, 1733, 1847, 1907, 1949, 2099, 2141, 2281, 2297, 2309, 2377, 2767, 3023, 3037, 3119, 3121, 3391, 3457
Offset: 1

Views

Author

Cino Hilliard, Nov 19 2003

Keywords

Examples

			In the decimal digits of Pi = 3.14159265... the first 2 occurs as the 7th digit, and 7 is prime; therefore a(1) = 7.

Crossrefs

Primes in A053746.
Cf. A088563 (similar for digits 0), A088565 (for digits 1),
Cf. A000796 (decimal digits of Pi).

Programs

  • PARI
    pizeros(n,d) = { default(realprecision,5000); p = Pi; v = Vec(Str(p)); for(x=1,n, if(v[x] == Str(d) && isprime(x-1),print1(x-1",")) ) }
  • PARI
    A088566_upto(N=3456, d=2)={localprec(N+20); [p|p<-primes([1, #N=digits(Pi\10^-N)]), N[p]==d]} \\ M. F. Hasler, Jul 28 2024

A373471 Primes indices of nonzero bits in Pi (A256108).

Original entry on oeis.org

3, 11, 13, 19, 23, 29, 41, 43, 47, 53, 71, 103, 107, 131, 149, 163, 173, 179, 197, 211, 227, 229, 239, 269, 281, 283, 293, 311, 349, 373, 379, 397, 409, 421, 457, 541, 557, 563, 577, 587, 599, 601, 607, 613, 617, 643, 647, 653, 659, 673, 709, 727, 733, 739, 743
Offset: 1

Views

Author

M. F. Hasler, Jul 27 2024

Keywords

Comments

Base 2 analog of A088565 (prime positions of '1's in decimal digits of Pi).

Examples

			Written in binary, Pi = 11.0010010000111111011010101000100010...[2] = Sum_{n >= -1} 2^-A256108(n), so the bits 1 have positions (-1, 0, 3, 6, 11, 12, 13, 14, 15, 16, 18, 19, 21, 23, 25, 29, 33, ...) and primes in this sequence are (3, 11, 13, 19, 23, ...) = this sequence.

Links

Crossrefs

Cf. A256108 (indices of nonzero bits in Pi), A004601 (Pi in base 2), A051480 (run lengths in A004601).
Cf. A088563 (indices of '0's in decimals of Pi).
Cf. A088565 (prime indices of '1's in the decimal digits of Pi).

Programs

  • Mathematica
    Select[PositionIndex[First[RealDigits[Pi, 2, 1000]]][1] - 2, PrimeQ] (* Paolo Xausa, Jul 31 2024 *)
  • PARI
    select(isprime, A256108_upto(777))
Showing 1-4 of 4 results.

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